Three capacitors of \( 2 \mu \mathrm{F}, 3 \mu \mathrm{F} \) and \(...

Three capacitors of \( 2 \mu \mathrm{F}, 3 \mu \mathrm{F} \) and \( 5 \mu \mathrm{F} \) are independently charged with batteries of emf's \( 5 \mathrm{~V}, 20 \mathrm{~V} \) and \( 10 \mathrm{~V} \) respectively. After disconnecting from the voltage sources. These capacitors are connected as shown in figure with their positive polarity plates are connected to \( \mathrm{A} \) and negative polarity is earthed. Now a battery of \( 20 \mathrm{~V} \) and an uncharged capacitor of \( 4 \mu \mathrm{F} \) capacitance are connected to the junction - A as shown with a switch \( \mathrm{S} \). When switch is closed, find :
- the potential of the junction \( \mathrm{A} \).
- final charges on all four capacitors.